The value of the given integral over the line segment c is -7/3.
What is line segment?A connected, non-empty set is what a line segment is. A closed line segment is a closed set in V if V is a topological vector space. However, if and only if V is one-dimensional, an open line segment is an open set in V.
To evaluate the given integral over the line segment c from (1, 1, 1) to (0, 4, 2), we need to parameterize the line segment and then perform the integration.
Let's parameterize the line segment c:
x = t, where t ranges from 1 to 0,
y = 1 + 3t, where t ranges from 1 to 0,
z = 1 + t, where t ranges from 1 to 0.
Now, we can rewrite the integral in terms of the parameter t:
∫c y d x y z d y ( y x ) d z = ∫(t, 1 + 3t, 1 + t) (y / x) dz.
Next, we need to find the limits of integration for t, which correspond to the endpoints of the line segment c. From (1, 1, 1) to (0, 4, 2), we have t ranging from 1 to 0.
Now, let's perform the integration:
∫c y d x y z d y ( y x ) d z
= ∫(t=1 to 0) ∫(z=1+t to 1+3t) (1 + 3t) / t dz dt.
First, we integrate with respect to z:
= ∫(t=1 to 0) [(1 + 3t) / t] (z) |(1+3t to 1+t) dt
= ∫(t=1 to 0) [(1 + 3t) / t] [(1 + 3t) - (1 + t)] dt
= ∫(t=1 to 0) [2t(1 + 2t)] dt
= ∫(t=1 to 0) [2t + 4t²] dt
= [t² + (4/3)t³] |(1 to 0)
= 0 - (1² + (4/3)(1³))
= -1 - (4/3)
= -7/3.
Therefore, the value of the given integral over the line segment c is -7/3.
Learn more about line segment on:
https://brainly.com/question/10496716
#SPJ4
10 to 9th power (inspired by mY FRIEND :)
Answer:
1000000000 is your answer
Just add 9 0's to the 1
Answer:
Hi........................
1) A Jet travels 520 miles in 2 hours. At this rate, how far could the jet fly in 13 hours? What is the rate of speed of the jet?
Answer:
\(Speed = \frac{distance}{time} = \frac{520}{2} =260miles \ per \ hour \\\\Distance = Speed * time = 260 * 13 = 3380miles\)
if f(x) equals 3X -2 what is f(5.9)
Answer:
f(5.9)= 15.7
Step-by-step explanation:
f(x) = 3x -2
f(5.9) = 3(5.9) -2
f(5.9) = 17.7 -2
f(5.9) = 15.7
Word Explination
If the (x) in f(x) is replaced by another variable (in this case, a number) any other x seen in the equation is replaced by that variable. For this question, the x in f(x) is replaced by 5.9. And so any other x in this equation needs to be replaced by 5.9 as well. From there on out, you solve.
Answer:
A) 9
Step-by-step explanation:
Edge 2022
In the table below, x represents miles traveled and y represents the cost to travel by train.
Miles, x
Cost, y
2
8.50
5
15.25
8
22.00
12
31.00
What is the y-intercept of this function?
2.25
4.00
6.50
17.13
Answer:
4.00
Step-by-step explanation:
Given
x: 2 , 5 , 8 , 12
y: 8.50, 15.25, 22.00. 31.00
Required
Determine the y intercept
First, we calculate the slope:
\(m = \frac{y_2- y_1}{x_2 - x_1}\)
Where
\((x_1,y_1) = (2,8,50)\)
\((x_2,y_2) = (12,31.00)\)
\(m = \frac{31.00 - 8.50}{12 - 2}\)
\(m = \frac{22.5}{10}\)
\(m = 2.25\)
Next, we calculate the equation:
\(y - y_1 = m(x - x_1)\)
Where:
\((x_1,y_1) = (2,8,50)\)
\(m = 2.25\)
The equation becomes:
\(y - 8.50 = 2.25(x - 2)\)
\(y - 8.50 = 2.25x -4.5\)
Make y the subject
\(y = 2.25x -4.5+8.50\)
\(y = 2.25x +4\)
Take \(x =0\); to get the y intercept
\(y = 2.25*0 +4\)
\(y = 4\)
Hence, the y intercept is 4.00
Answer:
The answer is B
Step-by-step explanation:
What is the average of 89, 91, and 84?
Answer:
88
Step-by-step explanation:
Use the following formula
Average=Sum/Count
89+91+84=264
264/3
88
Given that
P
=
7
x
+
20
−
2
y
.
Find
P
when:
x
=
7
and
y
=
10
Answer:
49 2 will be the answer
Step-by-step explanation:
when will u send me request in fb
Answer:
p = 49
hope it's helpful ❤❤❤❤❤
THANK YOU.
I borrow $5 from Luis and $ 8 from Stephanie.
How do I show my debt with integers.
Answer:
-5 + -8 = -13
Step-by-step explanation:
-5 + -8 = -13
in total you owe $13 but seperat it’s $5 and $8.
also you show a debt with Integers by using negative numbers.
Alex has a bucket in the shape of a cylinder. The diameter of the bucket is 12 inches and its height is 11.25 inches. How many buckets would it take ot fill an empty aquarium with 65 gallons of water? Show your work.
There would be 11 cylindrical buckets required to fill the empty aquarium with 65 gallons.
What is cylinder?A cylinder is three dimension solid, which has two circular base and which are connected by a curved surface.
Given that,
The diameter of cylindrical bucket d is 12 inches
so radius r=6 inches
And the height of bucket is 11.25 inches.
Volume of cylinder=π×r^2×h
Let n buckets are required to fill 65 gallons.
Since, 1 gallon = 231 inches,
65×231=n×22/7×6×6×11.25
15015×7=n×22×36×11.25
n=11.79
n=11 (approx.)
11 buckets will be required.
To know more on Cylinder:
https://brainly.com/question/865049
#SPJ1
Let R be the area bounded by a circular arc. x² + y2 = 1 above the x-axis Find the double integral ſf 3/2? +.y? JA using the coordinate transformation to the double integral in the polar coordinate
To find the double integral of f(x, y) = 3/2x + y² over the region R bounded by the circular arc x² + y² = 1 above the x-axis, we can use a coordinate transformation to convert the integral into polar coordinates.
In polar coordinates, the circular arc x² + y² = 1 corresponds to the equation r = 1, where r is the distance from the origin to a point on the curve. The region R can be represented in polar coordinates as 0 ≤ θ ≤ π, where θ is the angle measured from the positive x-axis to the point on the curve.
To perform the coordinate transformation, we substitute x = rcosθ and y = rsinθ into the integrand f(x, y):
f(x, y) = 3/2x + y²
= 3/2(rcosθ) + (rsinθ)²
= 3/2rcosθ + r²sin²θ.
The Jacobian determinant for the coordinate transformation from (x, y) to (r, θ) is r, so the double integral becomes:
∬R f(x, y) dA = ∫₀ᴨ ∫₀¹ (3/2rcosθ + r²sin²θ) r dr dθ.
Now, we can evaluate the double integral by integrating first with respect to r from 0 to 1, and then with respect to θ from 0 to π. This will give us the value of the integral over the region R bounded by the circular arc x² + y² = 1 above the x-axis.
To learn more about double integral click here: brainly.com/question/27360126
#SPJ11
Find the unite rate 380 19
Answer:
i have no clue
thank you so much for the points have a good day and im super sorry
Step-by-step explanation:
6b - 11 = -23 what is b
Answer:
8b-5=6b+23
8b-6b=23+5
2b=28
b=14
Step-by-step explanation:
Ethan is watering his plants. He starts with a watering can filled with 32 ounces of water, and he pours 3.5 ounces onto each plant. When Ethan finishes watering his plants, he has 14.5 ounces of water left. How many plants does he have? Write and solve an equation to find the answer.
The number of plants Ethan has are 5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the number of plants Ethan has.
Ethan uses 3.5 ounces of water for each plant, so he will use a total of 3.5p ounces of water.
If he starts with 32 ounces of water and ends up with 14.5 ounces
Total of 32 - 14.5 = 17.5 ounces of water.
As given the amount of water used is equal to the amount of water per plant times the number of plants:
3.5x = 17.5
Divide both sides by 3.5
x=5
Hence, , Ethan has 5 plants.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ9
Umm please help me wit this problem.
Answer:
1. 11
2. 3
Step-by-step explanation:
Hope this helps!! Have An Amazing Day!! Let me know if this is wrong.
HELP!!!Where does the graph of y = sin x from x = 0 to x = 2π start? A. at its minimum B. at an x–intercept C. at its maximum D. between an x–intercept and its maximum
Answer:
B. at an x–intercept
Step-by-step explanation:
You can find a graph of the sine function in numerous places.
y = sin(0) = 0
y = 0 for x = 0
so, on the given interval, it starts at an x-intercept.
Celo used the simple interest formula uppercase a = uppercase p (1 r t) to calculate the interest he earned on his savings last month. which equation is equivalent to the simple interest formula? uppercase p = startfraction uppercase a over 1 r t endfraction uppercase p = startfraction 1 r t over uppercase a endfraction uppercase p = uppercase a minus (1 r t) uppercase p = uppercase a (1 r t)
The equation equivalent to the simple interest formula A = P(1 + rt), that Celo used is P = A/(1 + rt). Hence, the first option is the right choice.
Equivalent equations are the equations that are transformed from one equation to another equation, but the final values they give are equal. It's just the change of the variable on which the equation is derived.
The simple interest equation that Celo used is A = P(1 + rt).
This is currently used to find the final amount A.
On isolating P to one side of the equation in the following ways:
A = P(1 + rt),
or, A/(1 + rt) = {P(1 + rt)}/(1 + rt) {Dividing both sides by (1 + rt)}.
or, A/(1 + rt) = P {Simplifying}.
or, P = A/(1 + rt) {Changing sides}.
Thus, the equation equivalent to the simple interest formula A = P(1 + rt), that Celo used is P = A/(1 + rt). Hence, the first option is the right choice.
Learn more about equivalent equations at
https://brainly.com/question/22441071
#SPJ4
The function shown models the depth d (in inches) of snow on the ground during the first 9 hours of a snowstorm, where t is the time (in hours) after the snowstorm begins
d(t)=1/2t+6
What is the domain
What is the range
The domain of the function d(t)=1/2t+6 is (-∞, ∞) and the range of the function is (-∞, ∞).
What are Domain and Range?Similar to how we input different numbers into functions, we also receive new numbers as the outcome. The two main characteristics of functions are domain and range.
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A → B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The set of images is the function's range.
The domain of the function d(t)=1/2t+6 is given by
Domain: (-∞, ∞), {x|x ∈ R}
The range of the function is given by
Domain: (-∞, ∞) , {y|y ∈ R}
To know more about the domain and range, visit:
https://brainly.com/question/28135761
#SPJ1
10. A coordinator at a local fundraiser has 14 volunteers to help out. There will be 3 volunteers working at the entrance door, 4 volunteers helping with the young children and 7 working at the tables with the fundraising activities.
a) In how many ways can the volunteers be assigned? [2]
b) Mary and Martha are new volunteers this year, so they should not be placed together. In how many ways can the volunteers be assigned so that Mary and Martha are not at the same station? [3]
The combination and permutations computed shows that the number of ways that the volunteers can be assigned is 120120.
How to calculate the combinationFrom the information given, the number of ways that the volunteers can be assigned will be:
= 14C3 × 11C4 × 7C7.
= (14 × 13 × 12)/6 × (11 × 10 × 9 × 8)/24
= 120120
Also, the number of ways that the volunteers can be assigned so that Mary and Martha are not at the same station will be:
= 12C1 × 11C4 × 7C7
= 12 × 330 × 1
= 3960
Learn more about permutations on:
https://brainly.com/question/1216161
Find the area of a rectangle with base of 2 yd and a height of 5 ft.
Possible Answers:
30 Square feet ⭐⭐⭐⭐⭐
10 Square Yards ⭐⭐⭐⭐⭐
12960 square inches ⭐⭐
8.36127 square meters ⭐
What is the value of the y-intercept of the graph f(x)=17⋅3.2^x ?
Answer:
f(0)=17
y-intercept=17
Step-by-step explanation:
Answer:
(0, 17) is the correct answer
Step-by-step explanation:
x^2 = 49, then x = 7. What would be a counterexample?
What is 8 (z + 8) expanded
8
+
6
4 HAVE A GREAT DAY!
What is the conditional probability that, when flipping a non-biased coin four times, there are at least two hs, given that the first flip is a h?
The conditional probability that, when flipping a non-biased coin four times, there are at least two heads, given that the first flip is a head, is 3/4.
Calculating the Conditional Probability:
Let us assume that getting a head in the first flip of coin is event B
Also, let us assume that getting a head in on of the remaining three flips is A
Then we have to find the probability of A given B, that is, P(A|B).
The formula for conditional probability is given as follows,
P(A|B) = P (A∩B) / P(B)
The probability of getting two heads, P(A∩B) = 3/8
The probability of getting head in the first flip, P(B) = 1/2
∴ P(A|B) = (3/8) / (1/2)
P(A|B) = 3/4
Thus, the conditional probability of getting at least two heads, given that the first flip is a head is 3/4.
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ4
determine the final price of an item that costs $75 and is 10% off show working
Answer:
67.5$
Step-by-step explanation:
75$ x .10 = 7.5$
75$ - 7.5$ = 67.5$
Answer:
$67.50
Step-by-step explanation:
First, find the discount.
Multiply the discount rate by the cost.
discount rate * cost
The discount rate is 10% and the cost is $75.
$75 * 10%
Convert 10% to a decimal. Divide 10 by 100 or move the decimal place two spots to the left.
10/100 = 0.10 or 10.0 --> 1.0 --> 0.10
$75 * 0.10
$7.5
Now, find the final price.
Since it is a 10% discount, we must subtract the discount amount from the cost.
cost - discount
The cost is $75 and the discount is $7.5
$75 - $7.5
$67.50
The final price of a item that costs $75 with a 10% discount is $67.50
can someone help me with this please
Answer:
The triangle is not isoceles, it's equilateral because all the sides are congruent. Isoceles has only 2 congruent sides.
x=4
y=12
Step-by-step explanation:
It's equilateral
5y=60
y=12
5x-6=3x+2
2x=8
x=4
Answer:
y= 12 x=4
Step-by-step explanation:
To find y.
Its an equilateral triangle.
Each angle is 5y.
Therefore 180, (degrees in a triangle) divided by 3, (angles) worth 5y means 180 divided (3x5y) = 180 divided by 15=12.
To find x rearrange 5x-6 = 3x-2 as all sides are the same length.
x=4
Find the length of the third side. If necessary, round to the nearest tenth.
The length of the third side is \(≈15.7\)
Step-by-step explanation:Note:
Phitagors theorem:
\(c^{2}=a^{2}+b^{2}\)
\(c: hypotenuse\)
\(a: altitude\)
\(b: base\)
1) Using Phitagors theorem
\(c^{2}=a^{2}+b^{2}\)
\(c^{2}=14^{2}+7^{2}\)
2) Calculate
\(c^{2}=245\)
3) Take the square root of both sides of the equation
\(\sqrt {c^{2}}=\sqrt{245}\)
\(c=\sqrt{245}\)
\(c≈15.7\)
Question
Example
Step by Step
In kite ABCD, mZBAE = 28° and mZBCE = 58°. Find mLABE.
Answer:
\(m\angle ABE=52^\circ\)
Step-by-step explanation:
Angles and Lines
The figure shows a kite ABCD where the following data is given:
\(m\BAE=28^\circ\)
\(m\BCE=58^\circ\)
We also know
\(BC\cong CD\)
\(AB\cong AD\)
Since triangle BCD is isosceles, it follows that:
\(m\angle CBE=m\angle CDE\)
And triangles BCD and DCE are congruent.
Thus:
\(m\angle BCE=m\angle DCE=58^\circ\)
And also:
\(m\angle BCE=58^\circ+58^\circ=116^\circ\)
Since the sum of internal angles of BCD is 180°
\(m\angle CDE=m\angle CBE= ( 180 - 116 ) / 2=32^\circ\)
The sum of angles of triangle CDE is 180°, thus
\(m\angle CED=180^\circ - 32^\circ - 58^\circ = 90^\circ\)
Angles CED and BEA are vertical (opposite), thus:
\(m\angle BCE=m\angle CED= 90^\circ\)
Finally, since the sum of the angles of triangle ABE is 180°
\(m\angle ABE= 180 - 90 - m\angle BAE\)
\(m\angle ABE= 180^\circ - 90^\circ - 28^\circ = 52^\circ\)
\(\mathbf{m\angle ABE=52^\circ}\)
at a price of $8 in this diagram, profit per unit is approximately , and total profit is approximately . $2.50; $36 $8.00; $114 $5.00; $60 $5.50; $78
The profit per bag is approximately $2.50 and the total profit is approximately is $36 , the correct option is (c) .
In the question ,
a graph of relation of price and quantity is given .
Under the perfect competition , the profit maximization condition is where price is equal to the marginal cost
that means P = MC .
price is given as = $8 ,
Form the graph ATC = $5.5
per unit profit can be calculated using the formula ,
Per unit profit = Price - ATC
per unit profit = 8 - 5.5
= $2.5
From the graph , the quantity is Q = 14.4 (approximately)
Total profit is calculated using the formula
Total Profit = (profit per unit) × (quantity)
Total Profit = 2.5 × 14.4
= $36
Therefore , The profit per bag is approximately $2.50 and the total profit is approximately is $36 .
The given question is incomplete , the complete question is
This figure is the market for bags of coffee roaster . At a price of $8 per bag . Profit per bag is approximately is and the total profit is .
(a) $5.50 , $78
(b) $5.00 , $60
(c) $2.50 , $36
(d) $8.00 , $114
Learn more about Profit here
https://brainly.com/question/17261352
#SPJ4
shaq is 85'' tal he cast a shadow 17''long if stephen curry cast a shadow 15''long how tall is he
Stephen Curry is 75 inches tall.
How to determine how long he isLet's call Stephen Curry's height h.
Since the shadow length of Shaq is proportional to his height,
we can write the following ratio:
shadow length of Shaq / Shaq's height = shadow length of Curry / Curry's height
This gives
17'' / 85'' = 15'' / h
Solving for h:
h = 15'' * 85'' / 17'' = 75''
So Stephen Curry is approximately 75 inches tall.
Read more about equivalent ratio at
https://brainly.com/question/2328454
#SPJ1
4. Show that the matrix [XX-X'Z(ZZ)-¹Z'X). where both the x & matrix X and the x matrix Z. have full column rank and m2, is positive definite. Discuss the implications of this result in econometrics.
To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.
Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:
A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'. The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric. Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v
Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.
When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.
To learn more about eigenvalues click here: brainly.com/question/29861415
#SPJ11
A farmer goes to the market to sell a box of eggs. A clumsy horse steps on the box of eggs and breaks a lot of them. The horse’s rider offers to pay for all of the eggs in the box and asks the farmer how many eggs there were. The farmer does not remember the exact number, but when she took them out of the box two at a time, there was 1 egg left. The same thing happened when she took them out three, four, five and six eggs at a time, but when she took them out 7 at a time, there were no eggs left
The smallest number of eggs that could have been in the box is 1134
The problem is to find the smallest number of eggs that could have been in the box, given the remainder when taking them out by different numbers. Here are the moves toward tackling it:
Allow n to be the quantity of eggs in the container. Then we have the accompanying arrangement of congruences:
n ≡ 1 (mod 2)
n ≡ 1 (mod 3)
n ≡ 1 (mod 4)
n ≡ 1 (mod 5)
n ≡ 1 (mod 6)
n ≡ 0 (mod 7)
For this problem, we have k = 6 k = 6, a i = {1,1,1,1,1,0} a_i = {1,1,1,1,1,0}, M i = {1260,840,630,504,420,720} M_i = {1260,840,630,504,420,720}, and y i = {−1,−2,−3,-4,-5,-6} y_i = {-1,-2,-3,-4,-5,-6}.
Plugging these values into the formula and simplifying modulo 5040, we get:
n = (−1260 + −1680 + −1890 + −2016 + −2100 + 0) mod 5040
n = (−8946) mod 5040
n = (−3906) mod 5040
n = 1134 mod 5040
Therefore, the smallest number of eggs that could have been in the box is 1134
to know more about congruences click here:
https://brainly.com/question/30818154
#SPJ4